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Article Dans Une Revue Mathematics and Computers in Simulation Année : 2001

Some experiments on the evaluation of functional ranges using a random interval arithmetic

René Alt
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Jean-Luc Lamotte
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Résumé

A software tool using standard and special interval arithmetic operations together with an idea which is developed in the discrete stochastic arithmetic (DSA) approach for round-off error evaluation is proposed in this paper for a statistical computation of functional ranges. The CESTAC method is a Monte Carlo method which uses DSA and provides the accuracy on any computed result with a high probability. On the other hand, interval computation gives a guaranteed interval containing the result but this interval may be in some cases useless because much too wide. Here it is proposed to combine both approaches to obtain a smaller but only highly probable interval containing the range of a rational function for given interval data. Various numerical experiments are given.

Dates et versions

hal-01149563 , version 1 (07-05-2015)

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René Alt, Jean-Luc Lamotte. Some experiments on the evaluation of functional ranges using a random interval arithmetic. Mathematics and Computers in Simulation, 2001, 56 (1), pp.17-34. ⟨10.1016/S0378-4754(00)00277-9⟩. ⟨hal-01149563⟩
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